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Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations

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Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations

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Arora, H.; Torregrosa Sánchez, JR.; Cordero Barbero, A. (2019). Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations. Mathematical and Computational Applications (Online). 24(1):1-15. https://doi.org/10.3390/mca24010003

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Título: Modified Potra-Pták multi-step schemes with accelerated order of convergence for solving sistems of nonlinear equations
Autor: Arora, Himani Torregrosa Sánchez, Juan Ramón Cordero Barbero, Alicia
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order ...[+]
Palabras clave: Systems of nonlinear equations , Iterative methods , Newton's method , Order of convergence , Computational efficiency , Basin of attraction
Derechos de uso: Reconocimiento (by)
Fuente:
Mathematical and Computational Applications (Online). (eissn: 2297-8747 )
DOI: 10.3390/mca24010003
Editorial:
MDPI AG
Versión del editor: https://doi.org/10.3390/mca24010003
Código del Proyecto:
info:eu-repo/grantAgreement/MINECO//MTM2014-52016-C2-2-P/ES/DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES./
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/
Agradecimientos:
This research was partially supported by Ministerio de Economia y Competitividad under grants MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089.
Tipo: Artículo

References

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Darvishi, M. T., & Barati, A. (2007). A fourth-order method from quadrature formulae to solve systems of nonlinear equations. Applied Mathematics and Computation, 188(1), 257-261. doi:10.1016/j.amc.2006.09.115

Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2009). A modified Newton-Jarratt’s composition. Numerical Algorithms, 55(1), 87-99. doi:10.1007/s11075-009-9359-z [+]
Homeier, H. H. . (2004). A modified Newton method with cubic convergence: the multivariate case. Journal of Computational and Applied Mathematics, 169(1), 161-169. doi:10.1016/j.cam.2003.12.041

Darvishi, M. T., & Barati, A. (2007). A fourth-order method from quadrature formulae to solve systems of nonlinear equations. Applied Mathematics and Computation, 188(1), 257-261. doi:10.1016/j.amc.2006.09.115

Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2009). A modified Newton-Jarratt’s composition. Numerical Algorithms, 55(1), 87-99. doi:10.1007/s11075-009-9359-z

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Grau-Sánchez, M., Grau, À., & Noguera, M. (2011). Ostrowski type methods for solving systems of nonlinear equations. Applied Mathematics and Computation, 218(6), 2377-2385. doi:10.1016/j.amc.2011.08.011

Grau-Sánchez, M., Noguera, M., & Amat, S. (2013). On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods. Journal of Computational and Applied Mathematics, 237(1), 363-372. doi:10.1016/j.cam.2012.06.005

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Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062

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